Section 10: Regression Equations Method

Regression equations are recommended as the
primary hydrologic method for off-system (non-TxDOT) projects; for
on-system projects, they are recommended as a check on other methods. Omega
EM regression equations are reliable beyond 10 sq. mi. drainage
area. A comparison method should be used for drainage areas below
10 sq. mi. and must be used for drainage areas below about 5 sq.
mi. This method should not be used for drainage areas less than
1 sq. mi.

Discretion may be used on off-system bridges and culverts.
As the design of these crossings is typically "hydraulically same
or slightly better," the importance of having an exact flowrate
is of lesser importance than on-system crossings. At the engineer's
discretion, the use of a comparison method may be disregarded.

If an adequate record of streamflow is not available at or
near the project site, an LPIII distribution cannot be developed
with Bulletin #17B procedures. An alternative for estimating the
needed design flow is to use a regression equation.

Regression equations are used to transfer flood characteristics
from gauged to ungauged sites through the use of watershed and climatic
characteristics as explanatory or predictor variables. USGS has
developed such regression equations for natural basins throughout
the State of Texas.

Procedure for Using Omega EM Regression Equations for Natural Basins

Equations have been developed for natural basins in 1-degree
latitude and longitude quadrangles in Texas. Figure 4-5 shows the
geographic extents of each quadrangle. The approach used to develop the
regional equations is referred to as the “Regression Equations for
Estimation of Annual Peak-Streamflow Frequency for Undeveloped Watersheds
in Texas Using an L-moment-Based, PRESS-Minimized, Residual-Adjusted
Approach.” (USGS 2009) For development and use of regression equations
a natural basin is defined as having less than 10 percent impervious
cover, less than 10 percent of its drainage area controlled by reservoirs,
and no other human-related factors affecting streamflow (USGS 2001).
The equations are therefore not applicable to urban watersheds.

Mean annual precipitation is the arithmetic mean of a suitably
long period of time of total annual precipitation in inches. The
mean annual precipitation was assigned based on the approximate
center of the watersheds. Asquith and Roussel (2009 TxDOT 0-5521-1)
considers that any general and authoritative source of mean annual
precipitation for any suitably long period (perhaps 30 years) is sufficient
for substitution into the regression equations.

Main channel length is defined as the length in stream-course
miles of the longest defined channel from the approximate watershed
headwaters to the outlet. Main channel slope is defined as the change
in elevation, in feet, between the two end points of the main channel
divided by the main channel length in feet.

Since the gauges used to develop the equations are points
in space, and that the variables used (contributing area, slope,
precipitation) are actually attributes of that specific point, the
OmegaEM should also pertain to the point in question. As such, if
the contributing drainage area overlaps more than one quadrant on
Figure 4-5, the OmegaEM must not be weighted or averaged. The OmegaEM specific
for the quadrant of the site must be selected.